Nuprl Lemma : pv11_p1_valid-ScoutState_wf
∀[Cmd:{T:Type| valueall-type(T)} ]
∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀accpts:bag(Id). ∀b:pv11_p1_Ballot_Num(). ∀e,start:E.
(((loc(e) = loc(start) ∈ Id) ⇒ start ≤loc e ) ⇒ (pv11_p1_valid-ScoutState(Cmd;accpts;b;start;es;e;f) ∈ ℙ))
Proof
Definitions occuring in Statement :
pv11_p1_valid-ScoutState: pv11_p1_valid-ScoutState(Cmd;accpts;b;start;es;e;f),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
subtype_rel: A ⊆r B,
listp: A List+,
name: Name,
vatype: ValueAllType,
prop: ℙ,
and: P ∧ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
pv11_p1_headers: pv11_p1_headers(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
subtract: n - m,
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
null: null(as),
pv11_p1_valid-ScoutState: pv11_p1_valid-ScoutState(Cmd;accpts;b;start;es;e;f),
pi2: snd(t)
Latex:
\mforall{}[Cmd:\{T:Type| valueall-type(T)\} ]
\mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}accpts:bag(Id). \mforall{}b:pv11\_p1\_Ballot\_Num().
\mforall{}e,start:E.
(((loc(e) = loc(start)) {}\mRightarrow{} start \mleq{}loc e )
{}\mRightarrow{} (pv11\_p1\_valid-ScoutState(Cmd;accpts;b;start;es;e;f) \mmember{} \mBbbP{}))
Date html generated:
2016_05_17-PM-04_10_45
Last ObjectModification:
2016_01_18-AM-11_14_22
Theory : paxos!synod
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